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58 lines
1.7 KiB
Markdown
58 lines
1.7 KiB
Markdown
# Empirical Hessian Receipt Pass
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## Purpose
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This implementation turns the Hessian-basis recompute from a heuristic routing table into measured curvature receipts.
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It uses `hessian-eigenthings` as the matrix-free curvature backend. The project rule is:
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```text
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do not materialize the full Hessian;
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query directional pressure via HVP/matvec;
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emit receipts for stiffness, flatness, saddle risk, and residual quality.
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```
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## Added files
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| Path | Purpose |
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| `5-Applications/tools-scripts/famm/hessian_receipt_runner.py` | CLI receipt runner around `hessian-eigenthings`. |
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| `shared-data/schemas/famm_hessian_curvature_receipt.schema.json` | Receipt schema. |
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| `shared-data/examples/famm_hessian_receipt_config.example.json` | Smoke-test config using a diagonal operator. |
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## Route rule
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The receipt runner maps measured curvature into route actions:
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| Curvature signal | Route action |
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| negative eigenvalues | `probe_saddle_scar` |
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| dominant eigenvalue above threshold | `protect_or_seal_stiff_invariant` |
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| enough near-zero eigenvalues | `press_flat_gauge` |
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| high trace | `seal_high_total_curvature` |
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| otherwise | `continue_measured_probe` |
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## Command
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```bash
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pip install hessian-eigenthings
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python3 5-Applications/tools-scripts/famm/hessian_receipt_runner.py \
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--config shared-data/examples/famm_hessian_receipt_config.example.json \
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--out shared-data/hessian-receipts/example_receipt.json
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```
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## Receipt role
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The output is not a proof. It is a computational witness that can update:
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```text
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proof priority
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compression priority
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scar-probe priority
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closure priority
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```
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## No-drift boundary
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A Hessian receipt can route work, rank scars, and justify pressure gates. It cannot replace exact Lean/Fraction/OISC proof receipts.
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